{
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   "source": [
    "## _*The Bernstein-Vazirani Algorithm*_ \n",
    "\n",
    "In this tutorial, we introduce the [Bernstein-Vazirani algorithm](http://epubs.siam.org/doi/abs/10.1137/S0097539796300921), which is one of the earliest algorithms demonstrating the power of quantum computing. Despite its simplicity, it is often used and is the inspiration for many other quantum algorithms even today; it is the basis of the power of the short-depth quantum circuits, as in [Bravyi et al.](https://arxiv.org/abs/1704.00690) that uses its non-oracular version, or in [Linke et al.](http://www.pnas.org/content/114/13/3305.full) that uses it to test the performance of the quantum processors (see also the [talk by Ken Brown](https://www.youtube.com/watch?v=eHV9LTiePrQ) at the ThinkQ 2017 conference). Here, we show the implementation of the Bernstein-Vazirani algorithm **without using entanglement** based on [Du et al.](https://arxiv.org/abs/quant-ph/0012114) on Qiskit and test it on IBM Q systems. \n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Rudy Raymond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction <a id='introduction'></a>\n",
    "\n",
    "The Bernstein-Vazirani algorithm deals with finding a hidden integer $a \\in \\{0,1\\}^n$ from an oracle $f_a$ that returns a bit $a \\cdot x \\equiv \\sum_i a_i x_i \\mod 2$ upon receiving an input $x \\in \\{0,1\\}^n$. A classical oracle returns $f_a(x) = a \\cdot x \\mod 2$ given an input $x$. Meanwhile, a quantum oracle behaves similarly but can be queried with superposition of input $x$'s. \n",
    "\n",
    "Classically, the hidden integer $a$ can be revealed by querying the oracle with $x = 1, 2, \\ldots, 2^i, \\ldots, 2^{n-1}$, where each query reveals the $i$-th bit of $a$ (or, $a_i$). For example, with $x=1$ one can obtain the least significant bit of $a$, and so on. This turns out to be an optimal strategy; any classical algorithm that finds the hidden integer with high probability must query the oracle $\\Omega(n)$ times. However, given a corresponding quantum oracle, the hidden integer can be found with only $1$ query using the Bernstein-Vazirani algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Algorithm\n",
    "\n",
    "The Bernstein-Vazirani algorithm to find the hidden integer is very simple: start from a $|0\\rangle$ state, apply Hadamard gates, query the oracle, apply Hadamard gates, and measure. The correctness of the algorithm is best explained by looking at the transformation of a quantum register $|a \\rangle$ by $n$ Hadamard gates, each applied to the qubit of the register. It can be shown that\n",
    "\n",
    "$$\n",
    "|a\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle.\n",
    "$$\n",
    "\n",
    "In particular, when we start with a quantum register $|0\\rangle$ and apply $n$ Hadamard gates to it, we have the familiar quantum superposition as below\n",
    "\n",
    "$$\n",
    "|0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle,\n",
    "$$\n",
    "\n",
    "which is slightly different from the Hadamard transform of the reqister $|a \\rangle$ by the phase $(-1)^{a\\cdot x}$. \n",
    "\n",
    "Now, the quantum oracle $f_a$ returns $1$ on input $x$ such that $a \\cdot x \\equiv 1 \\mod 2$, and returns $0$ otherwise. This means we have the following transformation:\n",
    "\n",
    "$$\n",
    "|x \\rangle \\left(|0\\rangle - |1\\rangle \\right) \\xrightarrow{f_a} | x \\rangle \\left(|0 \\oplus f_a(x) \\rangle - |1 \\oplus f_a(x) \\rangle \\right) = (-1)^{a\\cdot x} |x \\rangle \\left(|0\\rangle - |1\\rangle \\right). \n",
    "$$\n",
    "\n",
    "Notice that the second register $|0\\rangle - |1\\rangle$ in the above does not change and can be omitted for simplicity. In short, the oracle can be used to create $(-1)^{a\\cdot x}|x\\rangle$ from the input $|x \\rangle$. In this tutorial, we follow [Du et al.](https://arxiv.org/abs/quant-ph/0012114) to generate a circuit for a quantum oracle without the need of an ancilla qubit (often used in the standard quantum oracle). \n",
    "\n",
    "The algorithm to reveal the hidden integer follows naturally by querying the quantum oracle $f_a$ with the quantum superposition obtained from the Hadamard transformation of $|0\\rangle$. Namely,\n",
    "\n",
    "$$\n",
    "|0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle.\n",
    "$$\n",
    "\n",
    "Because the inverse of the $n$ Hadamard gates is again the $n$ Hadamard gates, we can obtain $a$ by\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The (Inner-Product) Oracle <a id='oracle'></a>\n",
    "\n",
    "Here, we describe how to build the oracle used in the Bernstein-Vazirani algorithm. The oracle is also referred to as the [inner-product oracle](https://arxiv.org/pdf/quant-ph/0108095.pdf) (while the oracle of the Grover search is known as the Equivalence, or EQ, oracle). Notice that it transforms $|x\\rangle$ into $(-1)^{a\\cdot x} |x\\rangle$. Clearly, we can observe that\n",
    "\n",
    "$$\n",
    "(-1)^{a\\cdot x} = (-1)^{a_1 x_1} \\ldots (-1)^{a_ix_i} \\ldots (-1)^{a_nx_n} = \\prod_{i: a_i = 1} (-1)^{x_i}. \n",
    "$$\n",
    "\n",
    "Therefore, the inner-product oracle can be realized by the following unitary transformation, which is decomposable as single-qubit unitaries: \n",
    "\n",
    "$$\n",
    "O_{f_a} = O^1 \\otimes O^2 \\otimes \\ldots \\otimes O^i \\otimes \\ldots \\otimes O^n, \n",
    "$$\n",
    "where $O^i = (1 - a_i)I + a_i Z$, where $Z$ is the Pauli $Z$ matrix and $I$ is the identity matrix for $a_i \\in \\{0,1\\}$. \n",
    "\n",
    "Notice that we start from a separable quantum state $|0\\rangle$ and apply a series of transformations that are separable (i.e., can be described by unitaries acting on a single qubit): Hadamard gates to each qubit, followed by the call to the *decomposable* quantum oracle as [Du et al.](https://arxiv.org/abs/quant-ph/0012114), and another Hadamard gate. Hence, there is no entanglement created during the computation. This is in contrast with the circuit at [Linke et al.](http://www.pnas.org/content/114/13/3305.full) that used CNOT gates to realize the oracle and an ancilla qubit to store the answer of the oracle. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Circuit <a id=\"circuit\"></a>\n",
    "\n",
    "We now implement the Bernstein-Vazirani algorithm with Qiskit by first preparing the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:43.600800Z",
     "start_time": "2018-09-26T15:37:42.133475Z"
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   },
   "outputs": [],
   "source": [
    "#initialization\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit.primitives import StatevectorSampler\n",
    "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
    "\n",
    "from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first set the number of qubits used in the experiment, and the hidden integer $a$ to be found by the Bernstein-Vazirani algorithm. The hidden integer $a$ determines the circuit for the quantum oracle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:45.913084Z",
     "start_time": "2018-09-26T15:37:45.909662Z"
    }
   },
   "outputs": [],
   "source": [
    "n_qubits = 14 # number of physical qubits\n",
    "a = 101      # the hidden integer whose bitstring is 1100101\n",
    "\n",
    "# make sure that a can be represented with nQubits\n",
    "a = a % 2**(n_qubits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then use Qiskit to program the Bernstein-Vazirani algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:47.277053Z",
     "start_time": "2018-09-26T15:37:47.265832Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f1f0582e500>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating registers\n",
    "# qubits for querying the oracle and finding the hidden integer\n",
    "qr = QuantumRegister(n_qubits)\n",
    "# for recording the measurement on qr\n",
    "cr = ClassicalRegister(n_qubits, name='res')\n",
    "\n",
    "bv_circuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "# Apply Hadamard gates before querying the oracle\n",
    "bv_circuit.h(qr)\n",
    "    \n",
    "# Apply barrier so that it is not optimized by the compiler\n",
    "bv_circuit.barrier()\n",
    "\n",
    "# Apply the inner-product oracle\n",
    "for i in range(n_qubits):\n",
    "    if (a & (1 << i)): # i.e. checking if the i-th bit of a is set to 1\n",
    "        bv_circuit.z(qr[i])\n",
    "    else:\n",
    "        bv_circuit.id(qr[i])\n",
    "        \n",
    "# Apply barrier \n",
    "bv_circuit.barrier()\n",
    "\n",
    "#Apply Hadamard gates after querying the oracle\n",
    "bv_circuit.h(qr)\n",
    "    \n",
    "# Measurement\n",
    "bv_circuit.barrier()\n",
    "bv_circuit.measure(qr, cr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:37:53.798709Z",
     "start_time": "2018-09-26T15:37:49.368851Z"
    }
   },
   "outputs": [
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RPovR17Ky81RSWlZtmzvjYFREuJLiY70e14svvqitW7dq8eLFXj/32Y7/eEr5J07V2O5OH0hpkyC7zeaVeFq3bq3vv/9eJSUluv3227Vo0SKvnPdsJJRRQ3FxsSZNmqR58+ape/fuRocDAGjEQux2vfbuR7UmFCXpdNEZPfPqe3U+7tKhrTq2S/J5nL5is1q1O+Ogtn31Ta3P11f/sNAQzbx1os/j9KXiklI9+9qaOm8OV981GDNsgNsJ5aeeekrz58/X6tWrDfswoVJYWIjWbPxMucd+qPX5+uqf0CpGd9x0jUtlRUdHa+fOnTp9+rQ++eQT/fGPf1RiYqJ+8YtfNKgODZWd+73e2/hZrc/VV3+LxaLbfza+3jLy8/N144036tlnn210Sz5YrRa9+OZalZTUPjuwvmswoHcXpSbX348rv+Ja6bLLLlN2drYeffRRQxPKIXabPv1it/Z++12tz9dX/+gmkbrThXHQ4XAoJiZGzz77rEJCQiRJJSUlmjRpkpYsWaKWLVs2sCaeO/lToV7819panzu3vrVtu25cmtsJ5aVLlyo5OblRLHMQGhqiN97/WD+eKqj1+fr6QIe2Sbr1ujG1HVrN66+/rqeeekrPPvusevfurYyMDP3ud7/TPffcY2hi3WqxKCPzsP69fVetz9dXf7vdphk3p7tU1osvvqhf/vKXSklJkdVqVadOnfTLX/5S//d//1dtVq6/lTkceu71NXI4PHstMGJwH3VoG7ivB8NCQ7Tu3zv0Xc6xWp+vr/5xLZvpty72gcYq7/vjevPDf9f6nCvj4C9cGAPc9dZbb2natGlatmyZLr74Yq+f/2x2m00rVq9X0ZniWp+vrw9c1K2DS68FXLV58+aqmfl33323WrVqpQceeMBr55dY8gK1yM3N1Z49e3THHXfIbrfLbrfrF7/4hcrLy2W32zV//nyjQwQANBJRkeGaOHqox8emjxri0myUhIQE5eVVnwF39OjRqueMNHb4IMU0b+rRseMvv0Qtm0V7OSL/atc6XkMH9PLo2OQLE3Rpvx5uHbNo0SLNnj1bq1ev1ogRIzwq15vsNpuuG5cmm839l9U2m1XXjUtzeTaK1WpVhw4d1LNnT91+++2aM2eO/vSnP7ldrrdd2q+Hki/07P/hsIG91LZ1/Qni3bt3KycnR+PGjat6ffrggw/qwIEDstvtevnllz0q3xtaNm+q8ZcPqn/HWsQ0b6oxaQM9LnvQoEHKysry+HhvsFgsmjBqiEuz7GszcdQQRUXUf2xCQoJSU1OrksmS1K1bN0nSoUOHPCrbW7qnJqtP91SPju3ZOUW9u3Zw65hTp05pxYoVuu222xrFbP3wsFBNHjtMnkQSHhaqSWOGyupCPWbNmqWZM2fq5z//uXr06KGJEydq/vz5Wrhwoc6cOeNB6d5z5ZB+uiC2hUfHjhk2QK3qmZ1cqW3btlq7dq0KCgr03Xffac+ePYqIiFDTpk0NvUFn0gWxGnlpX4+ObZ0Qp7RBF3klDqNeL9qsVk0el6aQer5xVxur1aLrxg2v99t6jV3Fh6MXenTsJX26q2M7704QeOWVV3TdddfpH//4h37+85979dy1aRodpWuvuNSjY5tFR+mqEd69H0hycrK6deumG2+8UYsWLdK8efNUWFjo1TJIKKOGpKQk7dq1Szt37qz6efDBB2Wz2bRz505NmzbN6BABAI1Ip/ZtNKB3F7ePSx81RE2iXFtWafDgwfrggw+qbXv//ffVtm1b42eohoZo8rg0t9/Ud+3YTn16eJaAaGxGXNrHpSULzhYWGqLJY4e5NaPqz3/+sx544AG99957jSKZXCk+rqWuHNLf7eNGDemv+DjPZ1U6HA7DkyhSRaJ70thhCgsNqX/nsyReEKPLB/dxad9+/frVeH16++2368ILL9TOnTsNX0O1b49O6tqxrVvHWCwWTR6X5vZ1O9sXX3yhCy/07A28N0VHRWrCqCFuHzfwoq7q1L6NS/tedtll+vbbb1VW9r+vVGdkZEhqHDfnGz/iknqX7ThXdJNIXXPFpW7//XjxxRdVUlKiW265xa3jfCmlTaIu7dfT7eOuueJSNXPxuhUWFtb4m2Gz2eR0Ouv8loy/hNjtmjwurd6la87VsV2SBl7cze3yIiMjlZiYqJKSEr3++uu65pprDJ2hLElDBvRSm0T3ZtqH2G26bqxnH8rWZvDgwVq7dq0cjv8tw/T+++8rMjJSF13knaR1XWJbNNO44e5/QDj8kovVOsG4DwO8xWKxaOLoIYoMD3PruLiWzTV6qPuvoc7nn//8p26++WY9//zzfkkmV+rZpb3bHxBK0qSxwxTh5nVzh8PhkMPhUElJSf07u4GEskkVFBRUvRgvKSlRXl6edu7cqW+//VYhISHq3r17tZ+kpIqvn3Tv3t3QTz4BAI3T2LSBimnh+izdvj07qWvHdi7v/7vf/U7btm3Tn/70J33zzTd6/vnntWTJEv3hD3/wIFrva5t0gYYN7O3y/k0iIzRh1GVuJRHO97fbaHabTde7MdNWkq4aMVgt3Jidfeedd+rRRx/V8uXL1alTJ+Xl5SkvL08nT570JGSvu7RfD6W0cX32U0qbBA12Y3b2fffdp3Xr1ungwYPKyMjQP//5Tz3yyCOaOnWqJ+F6Xctm0Ro/4hKX97fbKpIIrvaZqKioGq9PW7VqpdDQUHXv3l3Nmhm7DrnFYtGEK4eoSaTr9x4ZNrC32rqxzMFdd92lDRs26ODBg9q5c6fuuOMOrV27VnfeeacHEXtft47t1LdHJ5f3j23RTGOGDXB5/9///vf6/vvv9Zvf/EbffPONPvroI/3+97/XTTfdpBYtPJsZ6k3hYaEVHy66ccyk0UMV6cLs7HMtXbpU11xzjS64wL3kna9dMaSvW7N03Z2dfc0112jRokX617/+paysLH3wwQe65557NHr06EZx35+kC2I14lLXPiSTpIjwME0cM8yl2dmV1q5dq3fffVcHDx7Upk2bNHLkSBUVFTWKbxFXzNId5tZM2zFpA+tdO/ps9b0W+vWvf62TJ09q2rRp2rNnj1avXq17771Xv/3tb/1yU7b+vbqoU4rrH/Jd6MHs7PquQUlJSdXzBQUFOn78uHbu3Kmvv/7arXI80TQ6StdceZnL+1utFl033r2Z3fXV/4knntCvf/1rPfnkkxo6dGjV68Xjx4+7XR9PXDVysJpFu97XBvft7tZyL/XV/7HHHtO7776r/fv369tvv9Urr7yiOXPm6KqrrvL630qL0+iP8mCIjRs31nqXx6FDh2rjxo01tj/33HP65S9/WW1GAAAAZ/vuyFH9/aXV9c4SatksWjNvSa/35jvnevfddzV37lx98803io+P18yZM3XXXXc1JGSvKisv11PL31TO0drX0j3bTelXqmsH92Yzuvu32wibt/9H727YWu9+3VLb6cZrRrqVUK9r36lTp+q5555z+Ty+dOLkT1r8zOsqrmMt3UphoSG689aJbiXUf/e73+ntt9/WkSNHFB4erpSUFN166626/fbbZfPSDVwayul06sU312rPvqx69x07fKAu82A249nuv/9+vfjii43iQ5VKX+/P0gtvfFjvfkkXxOrXP7/arQ9hbrjhBm3evFnff/+9mjVrpp49e2ru3LkaPnx4Q0L2qjPFJXry2VU6UctNCs9mtVh0+41Xq01iK7fOv379ev3hD3/Qrl27FB8fr0mTJumBBx5QZGTjuZHVex9t1cfb/lPvfgMv6qprPPh69NatWzVo0CCtW7dOl19+uSch+lTOsR/0t+f/pXKH47z7Nf3v2tnuJNQLCwt1//33a9WqVcrJyVGrVq00btw4zZs3z9A1tM/mcDi09OW3dejI0Xr3vWH8cPVyczbjqlWr9Ic//EHfffedmjRpoiuvvFILFixQ27buvabwpc927tW/Pthc736pya11y6TRbr0WcOW10NatW3XXXXfpiy++UPPmzXXLLbdo3rx5fvtbeargtBY/85pOF9W+lm6lELtNM25JV1zL5m6dv75rkJWVpeTk5BrPt23b1m9LJK18Z4O+3FP/3+aRl/XV5Ze4t7ZxffVv165drcsg+fP18rdZR/T0ynfr3a9VTAv9duq1biXU66v/ww8/rOXLlysrK0tWq1Vt27bVz372M915551e/1tJQhkAAHjNhx9v14ZPv6zzeYukX025Su1cWDM1EB3NP6Elz71RdQfn2vTr2Vnpo93/anggcDidevqVd3Xwu5w692kSFaE7b53o1kzOQPL57n167d2N591n0thhHq+32tgVnC7S4mdeV0EdN+qUKr4a/8vrx7o1Ky+QvL5mk3b8J6PO5+02m3578wSP11tt7DIP5+ofL7+t873JHH7JxbriMs/WW23sysrK9X8v/Et539c9Gy62ZTPNmDpBoQ1Y7qQx27h1p97ftO28+9w6eYxXb0DVmPxw4pSefPZ1lZTWPRmrV5f2uuGqxveBgDc4nU49v+oDfXOg9ht1ShWzs39360Q1dWMmZyDZlXFQL7257rz7XHPFpRp4UVc/ReRfRWeKtfiZ13Xyp7rX7G2T2Eq/mnKV28vEBIq3132iLZ/vrvN5q9WiO266VkkXxPoxKu8KzpaD1+QczddPhaeNDgMAECAuH9xHSfF1vzAaMqBX0CaTJemC2BYadZ514Fo2j/Zofb1AYbVYNLmetXQnjh4atMlkSbq4W0d1S21X5/PdU5N1cbeO/gvIz5pERij9PGvpVq2dHaTJZEkaP3zQeW+2OWpY/6BNJksVN9sccp4bdSbFx7o9Iy2Q2O3nv1Gn1WLRdWPTgjaZLElD+vc879/6QRd3C9pksiTFtGiqcZfXvQRQ0yZRutrDm3cFAovFovRRQxQZUfeasNdecWnQJpMlqUenFF3cve6/9anJF3p0/5FAEREepkljh9X5fEiIXZPHur/meCAZNbT/eW+2OfLSvgGdTJZIKOM8HE6nXn13oxb+vxXad/Cw0eEAAAKAzWatWBfVXvNrhQmtYjy+A3gguaRvd7Vvm1hju8Vi0eSxaW4v9RFomjdtoqtH1n6n6v69OquzizfgClRVa+nWcsPJJlERuvZK99bODkRdOrRV/16da33umisudfvGZYEm7Dxr6XZom6RL+nT3e0z+NvLSvrXecLIi2TrcazfgaqwSWsXUOQM77ZKLdKGbS30EmsobddaWNI9r2Uyj3Vg7O1D169lJXTrU/vdu0pihbt+4LNBEN4nUhCtr/3Cxd9cO6tmlvZ8j8r+rRgyu9e9dZHiYJo4eEvSvBTq0TdLgvrX/vRubNlCxLY2994GvhYRU3KjTaq3Zzm0SLzjvB6+BIrj/knuBxWKp+o/+9ttva8SIEYqJiZHFYqm2/kpxcbGefPJJXXLJJWrevLnCw8PVqVMnzZ49W/n5+bWee+/evbrpppvUtm1bhYaGqmnTpkpJSdE111yjF1980R/VO689+zKV9/1xWa1WtQ7yFz0AAO9pFdtCo4dWf7Nos1l13bjaE83BxmqxaNKYYQo/J3E8NMhnZ5/tom4d1aNT9fX7Ypo31djhgwyKyL+iIsM1cfTQGtsnjh6qqEj3b8AViMYOH6SWzavP0u3RKdmju58Honat4zX0nBt1hoeFauKYoUE9O7uS3W7T9eNrJo5HDxtw3hlbweSyfjVn6baOj9PwQcE7O/tsMc2bavw5Y77VYtHkcWlu3bQtUFksFk0YNURR56wRfUmfbuoYxLOzz9a9U7IuPmd5p2bRUbqqjg+dg014WKgmjR1W48PFa668LKhnZ59t1JD+ahVT/Rs5nVKCe3b22VrHx+nywdVv1BkaYtfkccOCYnZ24NfATx577DFdddVV+uqrr9S+fXslJf3vLoxHjx7VoEGDdOedd+qzzz5T8+bNlZqaqkOHDmnRokXq06ePDh48WO18O3bsUN++fbV8+XLl5+erU6dOat++vU6dOqW33npL8+bN83cVq3E4nVq/5QtJ0qV9ewT9J6gAAO8a1KdbtTsWXzmkf62z1YLVubN0E1rFuHXn90BnsVh0zZWXKfq/s3QtLiyFEWw6t29T7Q3TgN5dgn529tnCQkN03di0qokZ0U0idY0JZmefbcSlfZTQKqbq8dUja5+tFqzi41rqysv6VT3u0DZJgy7uZmBE/mW1WjX5rFm6IfUshRGM+vbspC5n3YB2+CUX68IE80xUio6K1ISzlgCKa9lco4YG/+zss1014pJq496kMcNMlVto3yZRg/v1qHp8UbcO6tk5xcCI/CskxK7rxv9vlm5kRJjSRw811WuBYQN7V7sB7djhgxTbIjhmZ5vnr1kDzZ07V//3f/+no0ePatu2bTp8+LAGDRokp9Op6667Tl9++aXGjh2rAwcOKCsrS//5z3+Un5+vW2+9Vd99951uvPHGaud78MEHdfr0aU2dOlVHjx7Vrl279OWXXyo/P1/ffPONZs6caVBNK1TOTg4LDak2AAIA4IqKWbpDFR4WquQLE3SpCf+W9O7aQT06pchuq0gi2P10d/HGIirif7N0hw3spbYmmZ19tjFpAxXTvKliWjTVmLTgXTu7Lm1bx2vYwIqvdE6sZaZesKv8v2+zWdWzc4ppZmef7dJ+PZR8YULFTD2TzM4+W8vmTXXVf9fSHT1sgOJMMju7UuVaulGR4bowIU5pgy4yOiS/65baTn16pMpqteg6k8zOPlt4WKgm/3eW7uA+3dWhXVK9xwSbK4f00wWxLSpmZ48wx+zssyVdEFu15N21V16mpk0iDY7Iv2xWqyaPS1NIiF2d27epc0mwQGRxOp3nuwGv6VV+cnLHHXfo//7v/2o8/95772ns2LHq3r27tm/frvDw6i+Uy8vL1b9/f33xxRf697//rcGDKwaQzp07KyMjQ1999ZV69uzp1ZiXPP+Gfiqo+87arig4fVoOh1NhoSEKCw3utR4BAL5TWlYmm9UqaxB8rcsTDqdTZWVlCg0xz8zcc5WUlCokxG6q2ShnKysvlyTTfaBQyel0qrS0LKhvQFafktJShdjN+3/A4XCo3OFQiN1cibRKTqdTJaVlCjXxOFhaViar1RoUX/H2hNPpVKnZXwuYfBwsLy+X0ylTLP1Wm8px0EzfVDtXaWmZbLbG954oukmEfjt1gkfHmvOvugduvvnmWrevWrVKkjR16tQayWRJstlsuuqqq/TFF19o48aNVQnlCy+8UBkZGXr99dfVo0cPrw6sPxUU6VRBoVfOVVxSquKSUq+cCwAAszpTXGJ0CIY6U2Lu+oM+YPYxQJKKVGx0CIYqNvn/ATAOmL3+YBwMNiSUXdSlS+2Lhv/nP/+RJD377LN68803a93n6NGjkqQjR45Ubbvrrru0fv16PfTQQ3r++ec1atQoXXbZZUpLS6u2PrMnopvUvKu4O5idDAAAAAAAAASvhuQPWfKiHpUzh+u6TB07dtS3337r0rmmTp2q5557rurxhx9+qHnz5mnLli1yOBxV5Q0fPlyLFy9W9+7dGxa8B3ZlHNRLb65TWGiI7v71z0y1YD4AAAAAAACA8yOhXI/6EsoXXXSRdu7ctRcvEQAAA4FJREFUqdWrV2v8+PEelXHy5Elt2bJFGzdu1Msvv6wjR47oggsu0J49exQTE1P/Cc7RkDWUmZ0MAAAAAAAABDfWUDZQt27dtHPnTu3evdvjhHKzZs00ZswYjRkzRn/+85/Vq1cvHTx4UKtXr9Ytt9zi9vm8sYYyaycDAAAAAAAAOBcJ5QaaOHGiXnrpJf3jH//Qb3/7WzVp0qRB52vSpIl69uypgwcPKicnx6NzeLoGCrOTAQAAAAAAgODHGso+VN+SF06nU2lpadq0aZMGDRqkf/zjH9XWPnY4HPrss8/0/PPPa86cOUpJSZEkXXfddZoyZYquvPJKhYX9b53ijz76SFdddZUKCgq0Zs0ajRo1yoe1+x/WTgYAAAAAAABQHxLK9agvoSxJ+fn5uvrqq/XJJ59Iktq2bav4+HgVFRXpwIEDKiysWH5i79696ty5sySpefPmOnnypEJDQ9WhQwc1adJEubm5Onz4sCTp+uuv14oVK3xZtSoOp1N/fXaV8r4/rssvuVgjL+vrl3IBAP+/vTvUSTCAwjD8jU0DgYtgM1mwE7gGMoGb+y+AzUCxYqRZLCYqXAAwm0nnV5xje54bOCe/O9sBAACA2yIo/6IJyklyPp8zDEOGYch+v8/xeMx4PM50Os1ischyucx8Ps9oNEqSbDabbLfb7Ha7HA6HnE6nTCaTzGazrNfrrFarr9l/zXUyAAAAANAQlMnb+0eeX17z9PjgOhkAAAAA+JGgTJLkcrnmcr3m/s6fRgAAAADge4IyAAAAAACV0X8vAAAAAADAbRCUAQAAAACoCMoAAAAAAFQEZQAAAAAAKoIyAAAAAAAVQRkAAAAAgIqgDAAAAABARVAGAAAAAKAiKAMAAAAAUBGUAQAAAACoCMoAAAAAAFQEZQAAAAAAKoIyAAAAAAAVQRkAAAAAgIqgDAAAAABARVAGAAAAAKAiKAMAAAAAUBGUAQAAAACoCMoAAAAAAFQEZQAAAAAAKoIyAAAAAAAVQRkAAAAAgIqgDAAAAABARVAGAAAAAKAiKAMAAAAAUBGUAQAAAACoCMoAAAAAAFQEZQAAAAAAKoIyAAAAAAAVQRkAAAAAgIqgDAAAAABARVAGAAAAAKAiKAMAAAAAUBGUAQAAAACoCMoAAAAAAFQEZQAAAAAAKoIyAAAAAAAVQRkAAAAAgIqgDAAAAABA5RPaj6uRYcrxtwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1828.96x1287.61 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bv_circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment with Simulators\n",
    "\n",
    "We can run the above circuit on the simulator. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:38:02.785014Z",
     "start_time": "2018-09-26T15:38:02.562010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use local simulator\n",
    "sampler = StatevectorSampler()\n",
    "results = sampler.run([bv_circuit])\n",
    "counts = results.result()[0].data.res.get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the result of the measurement is the binary representation of the hidden integer $a$. \n",
    "\n",
    "## Experiment with Real Devices\n",
    "\n",
    "We can run the circuit on the real device as below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ibm_brisbane\n"
     ]
    }
   ],
   "source": [
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = service.least_busy(operational=True, simulator=False)\n",
    "print(backend.name)\n",
    "target = backend.target\n",
    "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n",
    "\n",
    "isa_circuit = pm.run(bv_circuit)\n",
    "#isa_circuit.draw(output='mpl',scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = Sampler(mode=backend)\n",
    "\n",
    "job = sampler.run([isa_circuit])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "service = QiskitRuntimeService()\n",
    "job = service.job('job id on quantum platform')\n",
    "job_result = job.result()\n",
    "counts = job_result[0].data.res.get_counts()\n",
    "#plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshold = int(0.01 * 1024) # the threshold of plotting significant measurements, 1% of the default number of shots, 1024\n",
    "filteredAnswer = {k: v for k,v in counts.items() if v >= threshold} # filter the answer for better view of plots\n",
    "\n",
    "removedCounts = np.sum([ v for k,v in counts.items() if v < threshold ]) # number of counts removed \n",
    "filteredAnswer['other_bitstrings'] = removedCounts  # the removed counts are assigned to a new index\n",
    "\n",
    "plot_histogram(filteredAnswer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We indeed see that the outcome is the binary representation of the hidden integer $a$ with high probability. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
